American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.

Abstract

Numerical simulation of a well in a vertically fractured reservoir is described. Real gas potential is the dependent variable. A fractional step numerical method which simultaneously integrates the difference expressions of the reservoir and fracture in an economical manner is used. Simulations of well performance with constant well potential and at several fracture extents are shown and discussed.

Introduction

The increasing demand for an adequate supply of natural gas has caused the development of extremely low permeability gas reservoirs. This is now possible because hydraulic fracturing can produce fractures with radii of 500 feet or more and thus stimulate production to levels that are economic. Estimation of the benefits to result from the hydraulic generation of a fracture in a particular formation is desirable.

It is the authors' belief that the numerical model given here is sufficiently novel and advantageous to merit attention.

Real gas potential is the dependent variable. The fracture is taken to occupy a negligible volume when compared to the volume of the reservoir. Then there is not the difficult problem of giving numerical representation of the small fracture width and the large reservoir extent in the one model. Yet one-dimensional Darcy flow is modeled in the fracture and two-dimensional Darcy flow is modeled in the reservoir. The numerical replacements of those differential expressions are solved simultaneously with relative ease.

The numerical method used is from a class of methods called fractional step methods. Some recent results show how these methods lend themselves to the treatment of third type boundary conditions such as occur for this problem. Also, it is recognized that numerical methods of this type may yield solutions that exhibit peculiar behavior near boundaries. peculiar behavior near boundaries.

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